Some further clarification questions:
Some of the suggestions here, regarding an associative Array-along-a-path, would require the things you're Moving to be equally spaced along the starting path object. It seems clear to me that this is not always going to be the case -- from your image, the lower two spacings here are clearly greater than the upper spacings:

If they can't be assumed to be equally spaced, I think the Array-along-a-path approach is not going to do what you want.
And I can't quite tell from the image, but are the objects to be Moved starting off at the same distance from the roadway-edge path object? Some of the suggestions involving Offsetting [I assume so the objects can be Moved to the nearest place on the Offset-result path] would do you no good if the objects are starting out at different distances from the path, and you want them at new but still different distances from it. [And you are correct -- a 3DPolyline cannot be Offset, anyway.]
My MPO command requires neither equal spacing nor starting or ending positions at equal distances from the path.
Kent Cooper, AIA